How can multiple Curves be used to control Camera movement?
You can animate the 'influence' value on each of the constraints you want to turn off. You can either animate the values off over a series of frames to fade the constraint's effects gradually or immediately.

The one thing to note is that when the object is no longer under the influence of the constraints it will return to the position it was at before it was constrained and will not stay at it's current position.

To counter this you can either reposition the object after the constraints are off or animate the 'influence' of some new constraints on at the same time as the old constraints are turning off.